alleryStart learning →Solve z² + 1 = 0:
- z = ±1
- z = -1
- z = ±i
- z = 1
Show answer and solution
Correct answer: C. z = ±i
We have z² = -1 → z.
So z² = ±i.
*Note: complex numbers were invented to give meaning to √(-1) = ±i.*
Indian Navy Pilot Complex Numbers — practice questions
Explore 6 free Complex Numbers questions in Indian Navy Pilot Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Complex Numbers with Quill →Complex Numbers questions and exercises with answers
Showing questions 1–6 of 6.
Solve z² + 1 = 0:Read the answer and worked solution →Compute (1 + i)⁸:Read the answer and worked solution →If z and z̄ are roots of a quadratic with real coefficients, then sum z + z̄ equals:Read the answer and worked solution →In z = a + ib, Re(z) and Im(z) areRead the answer and worked solution →The modulus $|3 + 4i|$ equals:Read the answer and worked solution →Which complex number has the larger modulus?Read the answer and worked solution →
Worked practice questions
Compute (1 + i)⁸:
- -16i
- 16
- 16i
- -16
Show answer and solution
Correct answer: B. 16
(1+i) = √2 cis(π/4).
**So (1+i)⁸ = (√2)⁸ × cis(8π/4) = 16 × cis(2π) = 16 × 1 = 16.**
If z and z̄ are roots of a quadratic with real coefficients, then sum z + z̄ equals:
- 2 Re(z) (twice real part)
- 0
- |z|
- Imaginary
Show answer and solution
Correct answer: A. 2 Re(z) (twice real part)
We have z + z̄ = (a + ib) + (a - ib).
That is z + z̄ = 2a.
So z + z̄ = 2 Re(z).
Complex conjugate pairs are roots of real-coefficient polynomials.
Sum and product of conjugates are both real.
How to practise
- Choose a Complex Numbers question and try to work out your answer.
- Open the question to check the correct answer and read its worked solution.
- Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.